A new loss function for multi-response optimization with model parameter uncertainty and implementation errors

Response surface-based design optimization has been commonly used to seek the optimal input settings in process or product design problems. Yet in most of the existing researches, there is no model parameter uncertainty in the modeling process and the optimal settings can be implemented at the precise values. These two assumptions are far from the reality. Consequently, the optimal settings often turn out to be suboptimal in some manner. This paper proposes a new loss function method to deal with model parameter uncertainty and implementation errors (MPUIE). An interpretable expression for the new optimization strategy is derived, which provides insights into the impact of MPUIE on the determination of the optimal settings. A random simulation example and a real-life case study are used to demonstrate the effectiveness of the proposed approach. The approach gives the optimal settings that are the result of making tradeoffs among different directions from the center of the experimental design region or, more generally, in a manner that mitigates the adverse effects of MPUIE.